“The president will know the number, and in each country how many — but not their names,” said Gordievsky, who said he spent nine years working in the KGB directorate in charge of illegal spy teams.

The FBI announced Monday the arrests of 10 alleged deep-cover Russian agents after tracking the suspects for years. They are accused of attempting to infiltrate U.S. policymaking circles while posing as ordinary citizens. All 10 are charged with conspiracy to act as an agent of a foreign government without notifying the U.S. attorney general — an offense that carries a maximum penalty of five years in prison.

An 11th person allegedly involved in the Russian spy ring was arrested Tuesday in Cyprus.

Countries often have a number of intelligence officials whose identities are declared to their host nation, usually working in embassies, trade delegations and other official posts.

Gordievsky said he estimates there are 400 declared Russian intelligence officers in the U.S., as well as up to 50 couples charged with covertly cultivating military and diplomat officials as sources of information. He said the complexity involved in training and running undercover teams means Russia is unlikely to have significantly more operatives now than during his career.

“I understand the resources they have, and how many people they can train and send to other countries,” Gordievsky said. “It is possible there may be more now, but not many more, and no more than 60 (couples).”

The ex-KGB official said deep cover spies often fail to deliver better intelligence than their colleagues who work in the open.

“They are supposed to be the vanguard of Russian intelligence,” Gordievsky said. “But what they are really doing is nothing, they just sit at home in Britain, France and the U.S.”

In Moscow, Russia officials called the U.S. arrests an unjustified throwback to the Cold War, and senior lawmakers said some in the U.S. government may be trying to undercut President Barack Obama’s warming relations with Moscow.

The Russian Foreign Ministry said Tuesday it was regrettable that the arrests came amid Obama’s push for a “reset” in Russian-U.S. ties.

“These actions are unfounded and pursue unseemly goals,” the Foreign Ministry said in a statement. “We don’t understand the reasons which prompted the U.S. Department of Justice to make a public statement in the spirit of Cold War-era spy stories.”

When asked if those arrested were Russian spies, the Russian Foreign Ministry and the foreign intelligence service refused to comment.

Foreign Minister Sergey Lavrov noted that U.S. authorities announced the arrest just days after Medvedev had visited the United States and met Obama at the White House.

“They haven’t explained to us what this is about,” Lavrov said at a news conference during a trip to Jerusalem. “I hope they will. The only thing I can say today is that the moment for doing that has been chosen with special elegance.”

Medvedev stopped by Washington last week after visiting high-tech firms in California’s Silicon Valley. The two presidents then went out for cheeseburgers, exchanged jokes and walked together in the park.

Nikolai Kovalyov, the former chief of the main KGB successor agency, the Federal Security Service, said some of the U.S. charges against the alleged spies resembled a “bad spy novel.”

Kovalyov, now a lawmaker, said the arrests were an attempt by some “hawkish circles” in the United States to demonstrate the need for a tougher line toward Moscow. Kovalyov added that Russian-U.S. ties will continue to improve despite the spy scandal.

“Our two great powers must stand together,” he said.

Some lawmakers suggested a tit-for-tat Russian response, but Kovalyov said Russia would reciprocate only “if the American don’t stop at that and risk evicting our diplomats,” the ITAR-Tass news agency reported.

Other senior Russian lawmakers also alleged that some in the U.S. government resented warmer ties with Russia.

“This was initiated, was done by certain people of certain political forces, who aren’t in favor of improving relations between Russia and the United States, and I feel deeply sorry about that,” Konstantin Kosachev, the head of the foreign affairs committee in the lower house, the State Duma, told The Associated Press Television News.

“Not all of them support Obama’s policy,” Mikhail Grishankov, a deputy head of the Duma’s security affairs committee told AP. “There are forces interested in tensions.”

Viktor Kremenyuk, a deputy head of the U.S. and Canada Institute, a Moscow-based think-tank, said the spy case could threaten a planned ratification of a new nuclear arms reduction deal signed by Obama and Medvedev in April.

“That may change the atmosphere, that may change the attitudes among Americans toward Russia, (and) that may cause very significant political consequences,” Kremenyuk said.

In Britain, the case stirred memories of the country’s own illegal Soviet spy — Melita Norwood, a civil servant who spent about 40 years passing atomic research and other secrets to Moscow. Authorities ruled against prosecuting the elderly grandmother when she was exposed in 1992. Norwood died in 2005 at the age of 93.

Britain and Ireland’s foreign ministries said Tuesday they are seeking clarification over the alleged use of forged passports by suspects arrested in the case by the FBI.

Documents filed at the U.S. District Court for the southern district of New York allege that suspect Richard Murphy used a false Irish passport and accuse suspect Tracey Lee Ann Foley of using a fraudulent British passport.

Ireland’s foreign ministry said it had asked the U.S. embassy in Dublin for confirmation. In London, the Foreign Office said it was checking the claim.